html - PHP - Send email from users address

I have a form on my website where users can type a message and their email, and it will be sent to my address. I have installed PHPMailer for another task, but I am using PHP's built in mail() function because I thought it would work better as it's only a simple task.

However, it does not seem to be working - emails are not sent. Here is my code:

$to = "myemail@gmail.com";
$subject = "Email from " . $_POST["name"];
$txt = $_POST["message"];

$headers = "From: " . $_POST["email"];

if (mail($to, $subject, $txt, $headers)) {
    // Success
} else {
    // Failed
}

Everything is posted correctly, it's just the mail() function that returns false. Why is this happening? Should I use PHPMailer instead?